The present invention relates generally to systems for processing measured signal values, and more specifically to systems for estimating parameter values relating to a set of measured signal values based on fuzzy logic techniques.
Systems for processing a number of measured signal values and determining a corresponding set of parameter values are known and commonly used in physical system modeling applications. Such applications are generally useful for aligning model parameters with test data resulting from the measured signal values.
An example of one known physical system modeling application 10 is illustrated in FIG. 1 and includes a physical system 12 having a number of physical processes associated therewith. A number, K, of physical process sensors 141-14K are suitably disposed relative to system 12, wherein K may be any positive integer. Sensors 141-14K are generally operable to sense operating conditions associated with physical system 12, and produce resulting operating condition signals (ci, i=1, . . . , K) on corresponding signal paths 161-16K. Application 10 further includes a performance analysis system 18 receiving the operating condition signals on signal paths 161-16K and determining predicted performance parameters therefrom. System 18 includes a pre-processing unit 20 having a first set of inputs electrically connected to the various physical process sensors 141-14K via signal paths 161-16K, a second number, L, of inputs electrically connected to a corresponding number, L, of outputs of a model-based parameter predictor block 30 via signal paths 361-36L, and a number, L, of outputs electrically connected to an equation solver 22 via a corresponding number, L, of signal paths 241-24L, wherein L may be any positive integer. Generally, K greater than L, and the pre-processor unit 20 is operable to combine one or more of the operating condition signals ci, i=1, . . . , K) to form a number, L, of corresponding operating parameter signals pj, j=1, . . . , L. The model-based parameter predictor block 36 is operable to produce L model parameter values mpj, j=1, . . . , L, wherein the model parameter values mpj, j=1, . . . , L correspond to the computed model values of the operating parameter signals pj, j=1, . . . , L. The pre-processor unit 20 is, in turn, operable to compute a number, L, of parameter delta values xcex4pj (j=1, . . . , L), wherein xcex4pj=pjxe2x88x92mpj, j=1, . . . , L, and to produce the parameter delta values xcex4pj on corresponding signal paths 241-24L.
System 18 further includes an equation solver block 22 having a first set of inputs receiving the parameter delta values xcex4pj (j=1, . . . , L) on signal paths 241-24L, a second set of inputs receiving a number of unknown variables xcex4xi and corresponding weighting factors Wji from the model-based parameter predictor block 30 via a number, N, of signal paths, wherein N may be any positive integer, and a set of outputs producing a number, J, of estimated values of the unknown variables xcex4xi, i=1, . . . , J.
The unknown variables xcex4xi, i=1, . . . , J represent functional distortions of the various components of physical system 12. For example, where performance analysis system 18 represents an engine performance modeling application, the functional distortions xcex4xi may correspond to compressor efficiency, turbine efficiency, flow capacity, pressure ratio, pressure drop, and the like, relating to one or more corresponding components of physical system 12. The weighting factors Wji correspond to the equation constants in the system of equations forming the particular model contained within the model-based parameter predictor block 30, wherein block 30 may include any number of models. In general, the equation solver 22 is thus operable to solve a system of equations of the form:
Wjixcex4xi=xcex4pj, i=1, . . . , J and j=1, . . . , L xe2x80x83xe2x80x83(1), 
where,
Wji=[∂pj/∂xi], j=1, . . . , L and i=1, . . . , J and define the various weighting factors linking the model parameter values mpi, i=1, . . . , L to the functional distortions xcex4xi, i=1, . . . , J.
The equation solver 22 is electrically connected to a set of inputs of a post processor unit 26 via signal paths 281-28J, and a set of inputs/outputs of post processor unit 26 are electrically connected to a corresponding set of inputs/outputs of the model-based parameter predictor 30 via a number, M, of signal paths 321-32M. In general, blocks 12, 20, 22, 26 and 30 form a closed-loop equation solving system using an iterative approach to compute a solution to the system of equations defined thereby. In this regard, the post-processor unit 26 is operable to receive from the model-based parameter predictor block 30 the estimated xcex4xi values from the previous iteration, to receive from the equation solver block 22 the estimated xcex4xi values from the present iteration, and compute an error vector xcex5k=xcex4xkxe2x88x92xcex4xkxe2x88x921, wherein k=iteration number. The post-processor block 26 is operable to halt the iterative equation solving process when xcex5k is within a desired range, and to accordingly notify the model-based parameter predictor 30 via one of the signal paths 321-32M.
The model-based parameter predictor 30 is electrically connected to a model storage and/or display unit 38 via a number, R, of signal paths 401-40R, wherein R may be any positive integer. Unit 38 may include a display and/or printer for viewing the results of the model, and may further include a data storage unit for recording the model results.
In the ideal case, the equation solver 22 can determine the correct or true solution associated with the unknown variables xcex4xi by solving any xe2x80x9cJxe2x80x9d of the xe2x80x9cLxe2x80x9d equations (assuming L greater than J) represented by equation (1) above. An example of such an ideal case is illustrated in FIG. 2 with L=5 and J=2. In this ideal case, the pre-processor unit 20 is operable to produce five parameter delta values (xcex4pj, j=1, . . . , 5), based on five corresponding measured operating conditions of physical system 12, and the model produced by the model-based parameter predictor 30 has two unknowns X and Y (e.g., xcex4x1 and xcex4x2). X and Y represent ratios and are therefore dimensionless. The true solution of the resulting system of equations 151-155 is defined by the intersection of equations 151-155, and is indicated on the plot of FIG. 2 by the point TS. The equation solver 22, in this example, can determine TS by solving a system of any two of the five equations 151-155 for the corresponding variables X and Y defining TS.
Due to limitations associated with known signal measurement instrumentation and with the physical application 10 in general, the ideal case illustrated in FIG. 2 typically does not occur. For example, measurement inaccuracies as well as model non-linearities each contribute to offsets in the measured operating condition signals on signal paths 161-16K, resulting in deviations in the system of equations from the true solution TS. A real-world representation of the example illustrated in FIG. 2 (e.g., L=5, J=2) is shown in FIG. 3 as a set of five system equations 171-175 having two unknowns X and Y. Due to instrumentation measurement inaccuracies as well as model non-linearities, equations 171-175 do not intersect at the true solution TS, but are instead offset therefrom by varying amounts as illustrated in FIG. 3.
In systems 10 of the type illustrated in FIG. 1, known Newton-type iterative techniques are typically used in the equation solver block 22 to solve the system of equations. The correction step for one such Newton technique is given by:
xcex5k=xe2x88x92W(x)xe2x88x921(xcex4xk)f(xcex4xk)xe2x80x83xe2x80x83(2), 
where,
k represents the number of the current iteration,
xcex5k=xcex4xxe2x88x92xcex4xk and is the correction vector representing the error between the exact solution xcex4x and its approximation xcex4xk at the kth iteration,
W(x)=fxe2x80x2(x)=[∂fj/∂xi], j=1, . . . L and i=1, . . . J and
f(x)=0 defines the system of non-linear equations.
For Newton-type methods, J=L such that the Jacobian matrix is square and non-singular, and the system of equations therefore has a unique solution at each iteration. The calculated solution at iteration k+1 is thus defined by:
xcex4xk+1=xcex4xkxe2x88x92W(x)xe2x88x921(xcex4xk)f(xcex4xk)xe2x80x83xe2x80x83(3), 
and the iterative calculations stop when xcex4xk+1xe2x88x92xcex4xkxe2x89xa6xcex50, where the error vector xcex50 is given.
One drawback associated with the use of Newton-type iterative algorithms of the type just described is that relatively low accuracy of the measurements of the parameters of the physical system 10 introduces random noise around the ideal performance parameter values, as illustrated by example in FIG. 3, and therefore distorts any deterministic solution of a square matrix-based linear system. Thus, while the foregoing Newton technique may produce a unique solution, this solution is very sensitive to instrumentation measurement inaccuracies and spurious readings, and may therefore be grossly inaccurate. What is therefore needed is an equation solving strategy that not only minimizes model non-linearities, as with the known Newton method, but also minimizes effects of instrumentation measurement inaccuracies and spurious readings.
The foregoing shortcomings of the prior art are addressed by the present invention. In accordance with one aspect of the present invention, a method of minimizing signal measurement inaccuracy effects in a signal processing system comprises assigning a probability distribution to each of a first number of delta values to form a corresponding first number of probability distribution functions, the delta values representing differences between pairs of measured signal values and corresponding model values, associating at least some of the first number of probability distribution functions with each equation in a system of equations defining a second number of unknown parameter values, solving the system of equations for a domain of possible solutions, and determining a unique solution for the second number of unknown parameter values from the domain of possible solutions.
In accordance with another aspect of the present invention, a method of minimizing signal measurement inaccuracy effects in a signal processing system comprises measuring a plurality of signal values, computing a first number of delta values each representing a difference between one of the plurality of signal values and a corresponding model value, assigning a probability distribution to each of the first number of the delta values to form a corresponding first number of probability distribution functions, associating at least some of the first number of probability distribution functions with each equation in a system of equations defining a second number of unknown parameter values, solving the system of equations for a domain of possible solutions, and determining a unique solution for the second number of unknown parameter values from the domain of possible solutions.
In accordance with a further aspect of the present invention, a system for minimizing signal measurement inaccuracy effects in a signal processing system comprises a plurality of sensors producing a corresponding plurality of signal values indicative of operating conditions of a physical system, and a signal processing system receiving the plurality of signal values, the signal processing system including means for assigning a probability distribution to each of a first number of delta values to form a corresponding first number of probability distribution functions, the delta values representing differences between pairs of measured signal values and corresponding model values, means for associating at least some of the first number of probability distribution functions with each equation of a system of equations defining a second number of unknown parameter values, means for solving the system of equations for a domain of possible solutions, and means for determining a unique solution for the second number of unknown parameter values from the domain of possible solutions.
In accordance with still another aspect of the present invention, a system for minimizing signal measurement inaccuracy effects in a signal processing system comprises a first circuit receiving a plurality of measured signal values and producing a first number of delta values each as a difference between one of the plurality of measured signal values and a corresponding model value, and a second circuit assigning a probability distribution to each of the first number of delta values to form a corresponding first number of probability distribution functions, the second circuit associating at least some of the first number of probability functions with each equation of a system of equations defining a second number of unknown parameter values and solving the system of equations for a domain of possible solutions, the second circuit producing a unique solution for the second number of unknown parameters based on the domain of possible solutions.
One object of the present invention is to provide a system for minimizing signal measurement inaccuracy effects in a signal processing system.
Another object of the present invention is to provide such a system by including a fuzzy logic estimator for solving systems of equations defined by a number of the measured signal values.
These and other objects of the present invention will become more apparent from the following description of the preferred embodiment.